Dynamic modeling and analysis of acute and chronic hepatitis B epidemic with saturation incidence

Abstract

The new stochastic and deterministic hepatitis B epidemic models are established. The models consist of four types: susceptible individuals, acutely infected hepatitis B individuals, chronically infected hepatitis B individuals and recovered individuals. This study focuses on the transmission dynamics of acute and chronic hepatitis B epidemics problems and the development of optimal control strategies to control the transmission of hepatitis B in the population. To this end, we first calculate the equilibrium point and basic reproduction number of the deterministic hepatitis B model to study the stability of the above model at the equilibrium point. Secondly, we give the basic reproduction number of the stochastic model of hepatitis B virus. A suitable Lyapunov function is constructed, and the solvability of the stochastic model is confirmed using the Itô formula. By using a series of stochastic inequalities and strong number theorems, the extinction and stationary distribution of hepatitis B in this stochastic model are obtained. Finally, the optimal control theory is used to develop an optimal control strategy for eliminating hepatitis B virus transmission. The Runge–Kutta method is used to simulate the above models to verify the rationality of our main theoretical results.